We'll brake up our solution finding, into simple steps....its the way that I
learned it, and I think its easier to follow this way.

o Step 1.

Equation of our Line

P(t) = P0 + t(P1 - P0)

This equation is also popularly known as a parametric line equation.

where

P0 is the starting point of our line

P1 is the end point of our line

t is variable which goes from 0 to 1, and is used to
derive a position at any point along our line.

o Step 2.

Equation for our Plane

N dot (Px - P2) = 0

where

Px is the point of intersection of our line

P2 is any point on the plane

N the normal for our plane

This equation is quit logical when you think about it, as when N and (Px-P2)
are at 90 degrees to each other. Remember (Px-P2) is the vector from P2 to
our intersection point.

o Step 3.

Substitute 1 into 2.

N dot (Px - P2) = 0

N dot { P0+t(P1-P0) - P2 } = 0

N dot { P0+t(P1-P0) } - N dot (P2) = 0

N dot { P0+t(P1-P0) } = N dot (P2)

N dot (P0) + N dot { t(P1-P0) } = N dot
(P2)

N dot { t(P1-P0) } = N dot { P2-P0 }

t is a constant so

t * N dot { P1-P0 } = N dot { P2-P0 }

t = N dot {P2-P0} / N dot
{P1-P0}

o Step 4.

We can substitute t back into our Line Equation to find the Point of
intersection Px.

P(t) = P0 + t(P1 - P0)

Px = P0 + [ N dot {P2-P0} /
N dot {P1-P0}] * (P1 - P0)

Notes.

We should test for our line being perpendicular to the plane at the start,
which usually means testing if Ndot(P1-P0)==0 , which tells us that our
line is never going to cross our plane.

t > 0 and t < 1 : The intersection occurs between the two end points
t = 0
: The intersection falls on the first end point
t = 1
: Intersection falls on the second end point
t > 1
: Intersection occurs beyond second end Point
t < 0
: Intersection happens before 1st end point.

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